A figure can normally attack once per action.
Most figures have two actions per turn.
This means that most figures may attack up to two times per turn.
This works the same for spells. Casting a spell normally takes one action, and figures usually have two actions per turn.
I'm saying "normally" or "usually" here, because if an attack or spell has the Cumbersome special ability, then it would take two actions to use that attack or spell.
The case may also exist where a figure has two or more seperate close combat attacks listed. In this case the figure may use each attack with the same attack action.
Hope this helps.
Kevin